Math 115                                             Name:                          Key

Quiz 3                                                  September 20, 2013

1.  Andy and Terry split a cake by the divider-chooser method.  Andy, the divider, likes chocolate icing twice as much as vanilla.  Show 2 different ways that Andy might split the cake to ensure he gets a “fair” piece.

1 option is to make each share contain                        Swap 1 choc for 2 white and it is still fair (to Andy)

2 choc, 2 white:           {7,8,1,2} / {3,4,5,6}               for example, {5,6,7,8,1} / {2, 3, 4} is fair

2.  Three players, Ali, Bo, and Caz, divide the 13 items shown by the method of markers.

 1       2      3         4        5       6      7        8        9       10     11    12   13

Which items: go to Ali? 9-13

go to Bo?  1 - 3

go to Caz?   6 -7

are (initially) left over? 4, 5, 8

2b.  According to the rules of this method, how should the leftovers be allocated?  EXPLAIN your answer in a complete English sentence.

Since everyone has received a fair share already, no matter what allocation of the leftovers is chose it will still be fair – so it doesn’t matter.

 Games Toys Clothes Alex 30 18 12 Brenda 36 16 20

3. 2 sisters, Alex and Brenda, divide some games, some clothes, and some toys by the method of sealed bids.

The bids (in \$) are as follows:

a.        Find the value of each sister’s fair share

Alex, 60/2= \$30

Brenda, 72/2 = \$36

b.      Determine what items each sister gets.  Then compute the payments in the first settlement, and finally determine the result after the final settlement.

Alex gets the toys (value of \$18 to her), Brenda gets the games and clothes (\$56 to her)

Brenda then pays \$20, while Alex takes \$12.  There is then an \$8 surplus, so each gets \$4 from that.  End result:  Alex gets the toys and \$16, Brenda gets the game and clothes, and pays \$16.